@article{Article_7,

title = {Lee Weight for Direct Sum of Codes},

journal = {Communications in Combinatorics, Cryptography & Computer Science},

volume = {2021},

issue = {1},

issn = { 2783-5456 },

year = {2021},

url = {http://cccs.sgh.ac.ir/Articles/2021/issue 1/1-7-lee_weight_for_direct_sum_of_codes-1637865461},

author = {Farzaneh Farhang Baftani},

keywords = {Linear code, Hamming Weight, Lee Weight, Generalized Lee Weight, Direct Sum of Codes.},

abstract = {Let C be a linear code of length n over Z4. The Lee support weight of C, denoted by wtL(C), is the sum of Lee weights of all columns of A(C) that A(C) is the jCj n array of all code words in C. For 1 6 r 6 rank(C), the r-th generalized Lee weight with respect to rank (GLWR) for C, denoted by dLr (C), is defined the minimum of all Lee weights of Z4-submodules of C with rank = r. In other words dLr (C) = minfwtL(D);D is a Z4 - submodule of C with rank(D) = rg For linear codes C1 and C2 over Z4 of length n1 and n2, respectively, the Direct Sum of them ,denoted by C1 C2 , is defined as follows: C1 C2 = f(c1, c2) : c1 2 C1, c2 2 C2g. Motivated by finding dLr (C1 C2) in terms of dLr (C1) and dLr (C2), we investigated dLr (C1 C2) and we obtained dLr (C1 C2) for r = 1, 2. Moreover, we generally obtained an upper bound for dLr (C1 C2) for all r, 1 6 r 6 rank(C1 C2).}

};